Timeline for Retracting off a compact set
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 19, 2020 at 1:12 | comment | added | erz | Thank you for your answer! Yeah, I also don't see how to apply this method to $n=3$: when you try to purify an edge, you spoil a face. | |
| May 17, 2020 at 10:59 | comment | added | Taras Banakh | @erz I have totally rewritten the solution but only for dimension 2. I am not sure if this approach will work for higher dimensions. One can try to understand what is going on for wild compact sets: horned Alexander sphere, wild Cantor set, Antoine necklage, etc. | |
| May 17, 2020 at 10:57 | history | edited | Taras Banakh | CC BY-SA 4.0 |
Totally rewritten solution
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| May 17, 2020 at 8:01 | comment | added | Taras Banakh | @erz I corrected the definition of $K^{(n)}$ so $K^{(2)}$ is now defined correctly as the set of 2-dimensional simplexes. Concerning the retraction, then indeed, there is a problem in my argument. I will think how to correct it. | |
| May 17, 2020 at 7:52 | history | edited | Taras Banakh | CC BY-SA 4.0 |
added 2 characters in body
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| May 17, 2020 at 2:53 | comment | added | erz | this is not much different from what i came up on my own, and here is where i was stuck all along: how to retract $\bar{\sigma}\backslash C$ onto $\partial\sigma\backslash C$? (by the way, i assume you meant $\sigma\in K^{(3)}$, right?) First, the latter set may be empty, even if the former is not (this can be solved by further dividing the cell). But what if the latter set is disconnected, while the former is connected? For example, imagine a triangle for which $C$ is an arc between two points in the triangle, but ventures into a neighboring triange. | |
| May 16, 2020 at 18:55 | history | answered | Taras Banakh | CC BY-SA 4.0 |